LAPACK 3.3.1 Linear Algebra PACKage

# dtpt01.f

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```00001       SUBROUTINE DTPT01( UPLO, DIAG, N, AP, AINVP, RCOND, WORK, RESID )
00002 *
00003 *  -- LAPACK test routine (version 3.1) --
00004 *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
00005 *     November 2006
00006 *
00007 *     .. Scalar Arguments ..
00008       CHARACTER          DIAG, UPLO
00009       INTEGER            N
00010       DOUBLE PRECISION   RCOND, RESID
00011 *     ..
00012 *     .. Array Arguments ..
00013       DOUBLE PRECISION   AINVP( * ), AP( * ), WORK( * )
00014 *     ..
00015 *
00016 *  Purpose
00017 *  =======
00018 *
00019 *  DTPT01 computes the residual for a triangular matrix A times its
00020 *  inverse when A is stored in packed format:
00021 *     RESID = norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS ),
00022 *  where EPS is the machine epsilon.
00023 *
00024 *  Arguments
00025 *  ==========
00026 *
00027 *  UPLO    (input) CHARACTER*1
00028 *          Specifies whether the matrix A is upper or lower triangular.
00029 *          = 'U':  Upper triangular
00030 *          = 'L':  Lower triangular
00031 *
00032 *  DIAG    (input) CHARACTER*1
00033 *          Specifies whether or not the matrix A is unit triangular.
00034 *          = 'N':  Non-unit triangular
00035 *          = 'U':  Unit triangular
00036 *
00037 *  N       (input) INTEGER
00038 *          The order of the matrix A.  N >= 0.
00039 *
00040 *  AP      (input) DOUBLE PRECISION array, dimension (N*(N+1)/2)
00041 *          The original upper or lower triangular matrix A, packed
00042 *          columnwise in a linear array.  The j-th column of A is stored
00043 *          in the array AP as follows:
00044 *          if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j;
00045 *          if UPLO = 'L',
00046 *             AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n.
00047 *
00048 *  AINVP   (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
00049 *          On entry, the (triangular) inverse of the matrix A, packed
00050 *          columnwise in a linear array as in AP.
00051 *          On exit, the contents of AINVP are destroyed.
00052 *
00053 *  RCOND   (output) DOUBLE PRECISION
00054 *          The reciprocal condition number of A, computed as
00055 *          1/(norm(A) * norm(AINV)).
00056 *
00057 *  WORK    (workspace) DOUBLE PRECISION array, dimension (N)
00058 *
00059 *  RESID   (output) DOUBLE PRECISION
00060 *          norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS )
00061 *
00062 *  =====================================================================
00063 *
00064 *     .. Parameters ..
00065       DOUBLE PRECISION   ZERO, ONE
00066       PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
00067 *     ..
00068 *     .. Local Scalars ..
00069       LOGICAL            UNITD
00070       INTEGER            J, JC
00071       DOUBLE PRECISION   AINVNM, ANORM, EPS
00072 *     ..
00073 *     .. External Functions ..
00074       LOGICAL            LSAME
00075       DOUBLE PRECISION   DLAMCH, DLANTP
00076       EXTERNAL           LSAME, DLAMCH, DLANTP
00077 *     ..
00078 *     .. External Subroutines ..
00079       EXTERNAL           DTPMV
00080 *     ..
00081 *     .. Intrinsic Functions ..
00082       INTRINSIC          DBLE
00083 *     ..
00084 *     .. Executable Statements ..
00085 *
00086 *     Quick exit if N = 0.
00087 *
00088       IF( N.LE.0 ) THEN
00089          RCOND = ONE
00090          RESID = ZERO
00091          RETURN
00092       END IF
00093 *
00094 *     Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0.
00095 *
00096       EPS = DLAMCH( 'Epsilon' )
00097       ANORM = DLANTP( '1', UPLO, DIAG, N, AP, WORK )
00098       AINVNM = DLANTP( '1', UPLO, DIAG, N, AINVP, WORK )
00099       IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
00100          RCOND = ZERO
00101          RESID = ONE / EPS
00102          RETURN
00103       END IF
00104       RCOND = ( ONE / ANORM ) / AINVNM
00105 *
00106 *     Compute A * AINV, overwriting AINV.
00107 *
00108       UNITD = LSAME( DIAG, 'U' )
00109       IF( LSAME( UPLO, 'U' ) ) THEN
00110          JC = 1
00111          DO 10 J = 1, N
00112             IF( UNITD )
00113      \$         AINVP( JC+J-1 ) = ONE
00114 *
00115 *           Form the j-th column of A*AINV
00116 *
00117             CALL DTPMV( 'Upper', 'No transpose', DIAG, J, AP,
00118      \$                  AINVP( JC ), 1 )
00119 *
00120 *           Subtract 1 from the diagonal
00121 *
00122             AINVP( JC+J-1 ) = AINVP( JC+J-1 ) - ONE
00123             JC = JC + J
00124    10    CONTINUE
00125       ELSE
00126          JC = 1
00127          DO 20 J = 1, N
00128             IF( UNITD )
00129      \$         AINVP( JC ) = ONE
00130 *
00131 *           Form the j-th column of A*AINV
00132 *
00133             CALL DTPMV( 'Lower', 'No transpose', DIAG, N-J+1, AP( JC ),
00134      \$                  AINVP( JC ), 1 )
00135 *
00136 *           Subtract 1 from the diagonal
00137 *
00138             AINVP( JC ) = AINVP( JC ) - ONE
00139             JC = JC + N - J + 1
00140    20    CONTINUE
00141       END IF
00142 *
00143 *     Compute norm(A*AINV - I) / (N * norm(A) * norm(AINV) * EPS)
00144 *
00145       RESID = DLANTP( '1', UPLO, 'Non-unit', N, AINVP, WORK )
00146 *
00147       RESID = ( ( RESID*RCOND ) / DBLE( N ) ) / EPS
00148 *
00149       RETURN
00150 *
00151 *     End of DTPT01
00152 *
00153       END
```